Modes of symmetric composite defects in two-dimensional photonic crystals

Publisher:
American Physical Society
Publication Type:
Journal article
Citation:
Dossou Kokou et al. 2009, 'Modes of symmetric composite defects in two-dimensional photonic crystals', American Physical Society, vol. 80, no. 1, pp. 013826-1-013826-14.
Issue Date:
2009
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We consider the modal fields and resonance frequencies of composite defects in two-dimensional photonic crystals (PCs). Using an asymptotic method based on Green's functions, we show that the coupling matrices for the composite defect can be represented as circulant or block-circulant matrices. Using the properties of these matrices, specifically that their eigenvectors are independent of the values of the matrix elements, we obtain modal properties such as dispersion relations, modal cutoff, degeneracy, and symmetry of the mode fields. Using our formulation, we investigate defects arranged on the vertices of regular polygons as well as PC ring resonators with defects arranged on the edges of polygons. Finally, we discuss the impact of band-edge degeneracies on composite-defect modes.
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